I got lots of private replies - thanks. The most informative one was that Hugo Volger published in 1975 a paper that includes "Higgs involution theorem", namely that any embedding of \Omega into itself is an involution (and hence an isomorphism). (1) Hugo Volger. "Ultrafilters, ultrapowers and finiteness in a topos". Journal of Pure and Applied Algebra 6 (1975) 345-356 (2) Then there is Johnstone's paper "Automorphisms of \Omega". Algebra Universalis, 9 (1979) 1-7. And then the references I mentioned below already when I asked the question, the Elephant and a paper by Freyd. It seems to me that the Higgs object was introduced by Johnstone in the above paper (and repeated in the Elephant). In the internal language, it is the object {q : \Omega | for all p : Omega, p or (p implies q)}. So the answers didn't uncover anything new, in terms of mathematics, but they include the new historical fact, to me, that it was Volger who first published Higgs' Involution Theorem. There doesn't seem to be anything published by Higgs himself about this. Best, Martin On 28/10/2023 21:03, Martin Escardo wrote: Dear topos theorists, Recently I found myself coming across Higgs' object. I only know two references that mention it, the Elephant, and Freyd's paper "Choice and well-ordering". Is there an original paper by Denis Higgs, or at least a manuscript by him that you may have seen or have available? When was the first time the Higgs' object showed up in topos theory? References or recollections are welcome. Thanks, Martin You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=files&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=leave&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>